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lilavasa [31]
2 years ago
9

Allyson and Adrian have decided to connect their ankles with a bungie cord; one end is tied to each person's ankle. The cord is

30 feet long, but can stretch up to 90 feet. They both start from the same location. Allyson moves 10 ft/sec north and Adrian moves 8 ft/sec west. There is a building with the nearest corner 30 ft north and 20 ft west of the girls' starting point. When will the bungie cord first touch the corner of the building?
Mathematics
1 answer:
BARSIC [14]2 years ago
3 0

Answer: 5.5 seconds

Step-by-step explanation:

30=5/4 ×(-20) + 10t

30 =-25 +10t

10t=55

t=5.5seconds

The cord will first touch the corner of the building after 5.5secs

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antiseptic1488 [7]

Answer:

y-5 = 3/2(x-3)

Step-by-step explanation:

The point slope form of the equation of a line is

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y-5 = 3/2(x-3)

7 0
3 years ago
Probabilities with possible states of nature: s1, s2, and s3. Suppose that you are given a decision situation with three possibl
amm1812

Answer:

1. P(s_1|I)=\frac{1}{11}

2. P(s_2|I)=\frac{8}{11}

3. P(s_3|I)=\frac{2}{11}

Step-by-step explanation:

Given information:

P(s_1)=0.1, P(s_2)=0.6, P(s_3)=0.3

P(I|s_1)=0.15,P(I|s_2)=0.2,P(I|s_3)=0.1

(1)

We need to find the value of P(s₁|I).

P(s_1|I)=\frac{P(I|s_1)P(s_1)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}

P(s_1|I)=\frac{(0.15)(0.1)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}

P(s_1|I)=\frac{0.015}{0.015+0.12+0.03}

P(s_1|I)=\frac{0.015}{0.165}

P(s_1|I)=\frac{1}{11}

Therefore the value of P(s₁|I) is \frac{1}{11}.

(2)

We need to find the value of P(s₂|I).

P(s_2|I)=\frac{P(I|s_2)P(s_2)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}

P(s_2|I)=\frac{(0.2)(0.6)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}

P(s_2|I)=\frac{0.12}{0.015+0.12+0.03}

P(s_2|I)=\frac{0.12}{0.165}

P(s_2|I)=\frac{8}{11}

Therefore the value of P(s₂|I) is \frac{8}{11}.

(3)

We need to find the value of P(s₃|I).

P(s_3|I)=\frac{P(I|s_3)P(s_3)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}

P(s_3|I)=\frac{(0.1)(0.3)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}

P(s_3|I)=\frac{0.03}{0.015+0.12+0.03}

P(s_3|I)=\frac{0.03}{0.165}

P(s_3|I)=\frac{2}{11}

Therefore the value of P(s₃|I) is \frac{2}{11}.

4 0
3 years ago
An escalator lifts people to the second floor of a building 25 feet above the first floor. The escalator rises at a 30 degree an
ch4aika [34]

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Answer:

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In this geometry, that means the length of the escalator is 2 times its height, so is ...

  x = 2(25 ft)

  x = 50 ft . . . . . distance a person travels

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